\RequirePackage{luatex85}
\documentclass{article}
\usepackage{pgfplots}
    \usepgfplotslibrary{groupplots}
    \pgfplotsset{
        % define the colormap
        colormap={parula}{
            rgb=(0.208100000000000,0.166300000000000,0.529200000000000)
            rgb=(0.969700000000000,0.848138095238095,0.147452380952381)
            rgb=(0.976300000000000,0.983100000000000,0.0538000000000000)
        },
    }
\begin{document}
    \begin{tikzpicture}
        \begin{groupplot}[
            group style={
                group name=G,
                group size=3 by 1,
                y descriptions at=edge left,
                horizontal sep=20pt % adjust as needed
            },
            enlargelimits=false,
            % !!! I don't know what the part `width("300")' is doing exactly !!!
            width=0.28\textwidth-width("300"),
            height=0.25\textheight,
            scale only axis,
            axis on top,
            grid=both,
        ]
        % add the colorbar to the first groupplot
        \nextgroupplot [
            % it should be horizontal ...
            colorbar horizontal,
            % ... and sampled
            colorbar sampled,
            % define the style of the colorbar
            colorbar style={
                % it should be positioned at ...
                at=(G c1r1.below south west),
                % ... with the anchor ...
                anchor=north west,
                % ... with the same width as the axis parts of the groupplots,
                % i.e. 3 times the width of a single groupplot plus two times
                % the width of the horizontal sep of the groupplots, ...
                parent axis width=3*(0.28\textwidth-width("300")) + 2*20pt,
                % ... and the start and end points ...
                point meta min=300,
                point meta max=1600,
                % ... and the number of samples should be identical to the
                % number of colors in the colormap
                samples={
                    \pgfplotscolormapsizeof{%
                        \pgfkeysvalueof{/pgfplots/colormap name}%
                    }+1
                },
            },
        ]
            \addplot graphics [xmin=0, xmax=50, ymin=0, ymax=150] {example-image-a};
        \nextgroupplot
            \addplot graphics [xmin=0, xmax=50, ymin=0, ymax=150] {example-image-b};
        \nextgroupplot
            \addplot graphics [xmin=0, xmax=50, ymin=0, ymax=150] {example-image-c};
        \end{groupplot}

%        % for debugging purposes only
%        \draw [red,very thin]
%            (G c1r1.south west) -- +(0,-1cm)
%            (G c3r1.south east) -- +(0,-1cm)
%        ;

    \end{tikzpicture}
\end{document}
